I was going to tell you how to disassemble the spindle, but you have now got it out.
But for the benefit of others who might have the same problem at some time or other, this is how it is done.
1. Push the spindle as far forwards as possible, until the woodruff key contacts the inner bearing shield.
2. Pull the bull gear and all the other bits that slide along the spindle backwards as far as they will go. This will allow to be seen just over half the length of the woodruff key.
3. Where the key touches the bearing shield, you can just get in under the end of the key something like a scriber or ice pick point. Flip up that front piece of the key so that it rotates in it's slot, allowing it to be pulled out with a pair of long nosed pliers. The spindle should then slide out past the nose rear bearing cover.
Putting it back together is great fun, taking hours sometimes to get the key back into it's slot, but there is an easy mod that I came up with when I had my Atlas 10F that you can do that makes things much easier.
Very gently remove the rear bearing cover from behind the nose bearing (it is a gentle tap out, and back in again), and file a small square slot into the edge of it where the key would normally fit against it. Don't file too deep, only just enough to allow the spindle to pass through with the key already fitted, otherwise oil will fly everywhere, as that cover helps to retain the oil around the bearing. Mount the cover with the filed slot at the top.
Once that little mod is done, it only usually takes a couple of minutes to disassemble and reassemble the spindle into the headstock.
I hope that explained it OK